Timeline for Controlling the tensor product of functions in $H^1$ with lower derivatives
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 31, 2023 at 15:47 | vote | accept | Víctor | ||
| Jul 31, 2023 at 15:14 | history | edited | Víctor | CC BY-SA 4.0 |
Corrected typo
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| Jul 31, 2023 at 15:13 | comment | added | Víctor | @WillieWong You're totally right, I want the RHS squared, thank you very much for pointing that out! | |
| Jul 31, 2023 at 14:02 | answer | added | Willie Wong | timeline score: 2 | |
| Jul 31, 2023 at 14:01 | comment | added | Willie Wong | In fact, if you just double $\phi$, then the left hand side quadruples while the right hand side doubles, based on what you wrote. So I shall assume that you meant for the RHS to be squared. | |
| Jul 31, 2023 at 13:49 | comment | added | Willie Wong | Did you perhaps want the RHS to be squared? | |
| Jul 31, 2023 at 13:47 | comment | added | Willie Wong | Let $D = [0,2\pi] \subset \mathbb{R}$. Let $\phi = \sin(k x)$ with $k \gg 1$, then any reasonable definition of $\|\phi\|_{\dot{H}^{1/2}}$ would be $\approx \sqrt{k}$. On the other hand $$ \|\phi \otimes \phi\|_{\dot{H^1}} \approx \|\phi\|_{L^2} \|\phi\|_{\dot{H}^1} \approx k $$ so what you want is impossible. | |
| S Jul 31, 2023 at 12:05 | review | First questions | |||
| Jul 31, 2023 at 12:13 | |||||
| S Jul 31, 2023 at 12:05 | history | asked | Víctor | CC BY-SA 4.0 |